In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models, however, either provide inconsistent predictions or require time-consuming aggregation process. We first prove the inconsistency of typical aggregations using disjoint or random data partition, and then present a consistent yet efficient aggregation model for large-scale GP. The proposed model inherits the advantages of aggregations, e.g., closed-form inference and aggregation, parallelization and distributed computing. Furthermore, theoretical and empirical analyses reveal that the new aggregation model performs better due to the consistent predictions that converge to the true underlying function when the training size approaches infinity.

为了扩展标准高斯过程回归到大规模数据集，聚合模型采用因子化训练过程，然后结合来自分布式专家的预测。然而，现有的聚合模型要么提供不一致的预测，要么需要耗时的聚合过程。本文对典型聚合方式使用不连续或随机数据划分的不一致性进行了证明，并提出了一种高效且一致性的大规模高斯过程聚合模型。所提出的模型继承了聚合的优点，如闭合形式推理和聚合，并行化和分布式计算。此外，理论和实证分析表明，由于预测一致，所以新的聚合模型在训练样本接近无穷大时会更加优越。

大规模高斯过程回归的普适稳健贝叶斯委员会机